\section{Methods}
\label{sec:method}
The previously presented models and derivations have been implemented in a combination of C++ and Python. Numerical procedures are implemented in a C++ module with a Python interface, a Python wrapper was implemented to facilitate ease of use. This section explains and summarises the relevant numerical methods and implementation specific equations used in this work. 

First, the numerical methods required to evaluate the integrals of Section \ref{sec:kin_dynamics} are covered. Later, in Sections \ref{subsec:method_steady_state} and \ref{sec:method_kempers_hs}, the Equations required for a closer analysis of the Kempers model and the assumptions behind it are presented.

\input{method/numerics}
\clearpage
\input{method/kempers_hs}
\newpage
\input{method/steady_state}
